What is the integral of y^2cos(x) ?

The integral of y^2cos(x) is y^2sin(x)+C

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integral of y^2cos(x)

\int y^{2} cos (x) d x

y^{2} sin (x) + C

Solution steps

\int y^{2} cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= y^{2} \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= y^{2} sin (x)

Add a constant to the solution

= y^{2} sin (x) + C

\frac{\partial}{\partial x} (x + \frac{y}{z})

y^{^{''}} - 8 y^{^{'}} + 17 y = 0

3 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

(1 + e^{x} y + x e^{x} y) d x + (x e^{x} + 2) d y = 0

\int \frac{9 x ^{3} - 5 x ^{2} + 3 x}{x} d x